Finite Group Databasebeta

← #23770526

Subgroups — #23770526

Order 10112.

416 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19098505C211yesmaximal, characteristic, complemented
2#19098505C211yesmaximal, characteristic, complemented
3#19098499C211yesmaximal, characteristic
4#19098484C211yesmaximal, characteristic, complemented
5#19098483C211yesmaximal, characteristic, complemented
6#19098475C211yesmaximal, characteristic
7#19098461C211yesmaximal, characteristic, complemented
8#19098459C211yesmaximal, characteristic, complemented
9#19098456C211yesmaximal, characteristic
10#19098450C211yesmaximal, characteristic, complemented
11#19098447C211yesmaximal, characteristic, complemented
12#19098438C211yesmaximal, characteristic
13#19098421C211yesmaximal, characteristic
14#19098421C211yesmaximal, characteristic
15#388×C79C211yesmaximal, characteristic
16C22×Dic158C2211yescharacteristic
17C23×Dic79C2211yescharacteristic
18C2×C4⋊Dic79C2211yescharacteristic
19C2×C4⋊Dic79C2211yescharacteristic
20C2×C4⋊Dic79C2211yescharacteristic
21C2×C4⋊Dic79C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2211yescharacteristic
24C2×Dic79⋊C4C2211yescharacteristic
25C2×Dic79⋊C4C2211yescharacteristic
26C2×Dic79⋊C4C2211yescharacteristic
27C2×Dic79⋊C4C2211yescharacteristic
28C2×C22⋊Dic79C2211yescharacteristic
29C2×C22⋊Dic79C2211yescharacteristic
30C2×C22⋊Dic79C2211yescharacteristic
31C2×C4×Dic79C2211yescharacteristic
32C79⋊#95C2211yescharacteristic
33C79⋊#95C2211yescharacteristic
34C79⋊#95C2211yescharacteristic
35C79⋊#95C2211yescharacteristic
36C79⋊#95C2211yescharacteristic
37C79⋊#95C2211yescharacteristic
38C79⋊#95C2211yescharacteristic
39C79⋊#95C2211yescharacteristic
40C79⋊#95C2211yescharacteristic
41C79⋊#95C2211yescharacteristic
42C79⋊#95C2211yescharacteristic
43C79⋊#95C2211yescharacteristic
44C2×C4⋊C4×C79C2211yescharacteristic
45C2×C22⋊C4×C79C2211yescharacteristic
46C2×C22⋊C4×C79C2211yescharacteristic
47C2×C22⋊C4×C79C2211yescharacteristic
48C2×C42×C79C2211yescharacteristic
49#95×C79C2211yescharacteristic
50#95×C79C2211yescharacteristic
51C2×Dic158—41no—
52C2×Dic158—41no—
53C2×Dic158—41no—
54C22×Dic79—22no—
55C22×Dic79—22no—
56C22×Dic79—41no—
57C22×Dic79C2311yescharacteristic
58C22×Dic79C2311yescharacteristic
59C22×Dic79C2311yescharacteristic
60C22×Dic79C2311yescharacteristic
61C22×Dic79C2311yescharacteristic
62C22×Dic79C2311yescharacteristic
63C22×Dic79C2311yescharacteristic
64C22×Dic79C2311yescharacteristic
65C4⋊Dic79—22no—
66C4⋊Dic79—22no—
67C4⋊Dic79—41no—
68C4⋊Dic79—41no—
69Dic79⋊C4—22no—
70Dic79⋊C4—22no—
71Dic79⋊C4—41no—
72Dic79⋊C4—41no—
73Dic79⋊C4—41no—
74Dic79⋊C4—41no—
75C22⋊Dic79—41no—
76C22⋊Dic79—41no—
77C22⋊Dic79—41no—
78C4×Dic79—41no—
79C24×C79C2311yescharacteristic
80C22×C4×C79C2311yescharacteristic
81C22×C4×C79C2311yescharacteristic
82C22×C4×C79C2311yescharacteristic
83C22×C4×C79C2311yescharacteristic
84C22×C4×C79C2311yescharacteristic
85C22×C4×C79C2311yescharacteristic
86C4⋊C4×C79—41no—
87C22⋊C4×C79—41no—
88C22⋊C4×C79—41no—
89C22⋊C4×C79Q814yescomplemented
90C42×C79—41no—
91C23×C79—21no—
92C23×C79—21no—
93C23×C79—21no—
94C23×C79—21no—
95C23×C79—21no—
96C23×C79—21no—
97C23×C79C2×Q812yes—
98C23×C79C2411yescharacteristic
99C2×C4×C79—21no—
100C2×C4×C79—21no—
101C2×C4×C79—21no—
102C2×C4×C79—21no—
103C2×C4×C79—21no—
104C2×C4×C79—21no—
105C2×C4×C79—21no—
106C2×C4×C79—21no—
107C2×C4×C79—21no—
108C2×C4×C79—21no—
109C2×C4×C79—21no—
110C2×C4×C79—21no—
111C2×C4×C79—21no—
112C2×C4×C79—21no—
113C2×C4×C79—21no—
114C2×C4×C79—21no—
115C2×C4×C79C2×Q812yes—
116C2×C4×C79C2×Q812yes—
117C2×Dic79—21no—
118C2×Dic79—21no—
119C2×Dic79—21no—
120C2×Dic79—21no—
121C2×Dic79—21no—
122C2×Dic79—21no—
123C2×Dic79—21no—
124C2×Dic79—21no—
125C2×Dic79—21no—
126C2×Dic79—21no—
127C2×Dic79—21no—
128C2×Dic79—21no—
129C2×Dic79—21no—
130C2×Dic79—21no—
131C2×Dic79—21no—
132C2×Dic79—21no—
133C2×Dic79—21no—
134C2×Dic79—21no—
135C2×Dic79—21no—
136C2×Dic79—21no—
137C2×Dic79—21no—
138C2×Dic79—21no—
139C2×Dic79—44no—
140C2×Dic79#4112yes—
141C2×Dic79#4112yes—
142Dic158—44no—
143C22×C79—22no—
144C22×C79—22no—
145C22×C79—22no—
146C22×C79—41no—
147C22×C79—41no—
148C22×C79—41no—
149C22×C79—41no—
150C22×C79C22×Q811yescharacteristic
151C22×C79C2×#4111yescharacteristic
152C22×C79C2×#4111yescharacteristic
153C22×C79H(5,𝔽2)11yescharacteristic
154C22×C79H(5,𝔽2)11yescharacteristic
155C22×C79H(5,𝔽2)11yescharacteristic
156C22×C792−1+411yescharacteristic
157C4×C79—22no—
158C4×C79—22no—
159C4×C79—41no—
160C4×C79—41no—
161C4×C79—41no—
162C4×C79—41no—
163Dic79—22no—
164Dic79—22no—
165Dic79—41no—
166Dic79—41no—
167Dic79—41no—
168Dic79—41no—
169Dic79—41no—
170Dic79—41no—
171C2×C79—42no—
172C2×C79#54211yescharacteristic
173C2×C79#54211yescharacteristic
174C2×C79#54411yescharacteristic
175C2×C79#55111yescharacteristic
176C2×C79#55411yescharacteristic
177C2×C79#55411yescharacteristic
178C2×C79#56011yescharacteristic
179#2742—791nomaximal, Sylow
180C79#274211yescharacteristic, complemented, Sylow
181#400—791no—
182#400—791no—
183#399—791no—
184#395—791no—
185#395—791no—
186#393—791no—
187#389—791no—
188#389—791no—
189#388—791no—
190#388D7911yescharacteristic
191#387—791no—
192#387—791no—
193#385—791no—
194#380—791no—
195#380—791no—
196C22×Q8—791no—
197C23×C4—791no—
198C2×C4⋊C4—791no—
199C2×C4⋊C4—791no—
200C2×C4⋊C4—791no—
201C2×C4⋊C4—791no—
202C2×C4⋊C4—791no—
203C2×C4⋊C4—791no—
204C2×C4⋊C4—791no—
205C2×C4⋊C4—791no—
206C2×C4⋊C4—791no—
207C2×C4⋊C4—791no—
208C2×C4⋊C4C2×D7911yescharacteristic
209C2×C22⋊C4—791no—
210C2×C22⋊C4—791no—
211C2×C22⋊C4—791no—
212C2×C22⋊C4C2×D7911yescharacteristic
213C2×C22⋊C4C2×D7911yescharacteristic
214C2×C22⋊C4C2×D7911yescharacteristic
215C2×C42—791no—
216C2×C42C2×D7911yescharacteristic
217#95—791no—
218#95—791no—
219#95—791no—
220#95—791no—
221#95—791no—
222#95—791no—
223#95—791no—
224#95—791no—
225#95—791no—
226#95—791no—
227#95—791no—
228#95—791no—
229#95C2×D7911yescharacteristic
230#95C2×D7911yescharacteristic
231C24C22×D7911yescharacteristic
232C2×Q8—3161no—
233C2×Q8—3161no—
234C2×Q8—3161no—
235C22×C4—3161no—
236C22×C4—791no—
237C22×C4—791no—
238C22×C4—791no—
239C22×C4—791no—
240C22×C4—791no—
241C22×C4—791no—
242C22×C4—791no—
243C22×C4—791no—
244C22×C4—1582no—
245C22×C4—1582no—
246C22×C4C22×D7911yescharacteristic
247C22×C4C22×D7911yescharacteristic
248C22×C4C22×D7911yescharacteristic
249C22×C4C22×D7911yescharacteristic
250C22×C4C22×D7911yescharacteristic
251C22×C4C22×D7911yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—3161no—
254C4⋊C4—3161no—
255C4⋊C4—3161no—
256C4⋊C4—3161no—
257C4⋊C4—3161no—
258C4⋊C4—3161no—
259C4⋊C4—1582no—
260C4⋊C4—1582no—
261C4⋊C4—1582no—
262C4⋊C4—1582no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—3161no—
266C22⋊C4—3161no—
267C22⋊C4—3161no—
268C22⋊C4Dic15814yescomplemented
269C42—41no—
270C42—3161no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23C2×Dic15812yes—
278C23C23×D7911yescharacteristic
279Q8—3164no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—3164no—
297C2×C4—792no—
298C2×C4—792no—
299C2×C4—1581no—
300C2×C4—1581no—
301C2×C4—1581no—
302C2×C4—1581no—
303C2×C4—1581no—
304C2×C4—1581no—
305C2×C4—1581no—
306C2×C4—1581no—
307C2×C4—1581no—
308C2×C4—1581no—
309C2×C4—1581no—
310C2×C4—1581no—
311C2×C4—1581no—
312C2×C4—1581no—
313C2×C4—1581no—
314C2×C4—1581no—
315C2×C4—1581no—
316C2×C4—1581no—
317C2×C4—1581no—
318C2×C4—1581no—
319C2×C4—1581no—
320C2×C4—1581no—
321C2×C4C2×Dic15812yes—
322C2×C4C2×Dic15812yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×Dic15811yescharacteristic
331C22#41×D7911yescharacteristic
332C22#41×D7911yescharacteristic
333C22#1457920611yescharacteristic
334C22#1457920611yescharacteristic
335C22#1457920711yescharacteristic
336C22#1457920811yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3161no—
344C4—3161no—
345C4—3161no—
346C4—3161no—
347C4—3161no—
348C4—3161no—
349C4—1582no—
350C4—1582no—
351C2—42no—
352C2#1909917711yescharacteristic
353C2#1909918111yescharacteristic
354C2#1909919111yescharacteristic
355C2#1909923811yescharacteristic
356C2#1909927211yescharacteristic
357C2#1909927211yescharacteristic
358C2#1909930111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#388×C79C2
prime radicalC24×C79C23
hypercenter#388D79
hypocenterC79#2742
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19098505C2semidirect
2. #19098505C2semidirect
4. #19098484C2semidirect
5. #19098483C2semidirect
7. #19098461C2semidirect
8. #19098459C2semidirect
10. #19098450C2semidirect
11. #19098447C2semidirect
89. C22⋊C4×C79Q8semidirect
180. C79#2742semidirect
268. C22⋊C4Dic158semidirect